{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3CXPDSHOOWLTMIRTLQ54JUYLDU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"668553415e629b8b96bfadb43837a105ec8f4fcad940543538eb4f8219d63bac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T13:52:42Z","title_canon_sha256":"cdd38288afe3fb260e64a8ddfab978ca316d02caa966239fa8918a838214ce78"},"schema_version":"1.0","source":{"id":"1511.06168","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06168","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06168v5","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06168","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"3CXPDSHOOWLT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3CXPDSHOOWLTMIRT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3CXPDSHO","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:526addc80e6fb0471d8127846b54765c626fd8775da1dee04e32d527a77ee136","target":"graph","created_at":"2026-05-18T00:54:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For every H-space $X$ the set of homotopy classes $[X,X]$ possesses a natural algebraic structure of a loop near-ring. Albeit one cannot say much about general loop near-rings, it turns out that those that arise from H-spaces are sufficiently close to rings to have a viable Krull--Schmidt type decomposition theory, which is then reflected into decomposition results of H-spaces. In the paper we develop the algebraic theory of local loop near-rings and derive an algebraic characterization of indecomposable and strongly indecomposable H-spaces. As a consequence, we obtain unique decomposition the","authors_text":"Damir Franeti\\v{c}, Petar Pave\\v{s}i\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T13:52:42Z","title":"Loop near-rings and unique decompositions of H-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06168","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8f4e65af55da1121be7ba7459e32e097bef0990d00433dab6c0a02d9843e2301","target":"record","created_at":"2026-05-18T00:54:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"668553415e629b8b96bfadb43837a105ec8f4fcad940543538eb4f8219d63bac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T13:52:42Z","title_canon_sha256":"cdd38288afe3fb260e64a8ddfab978ca316d02caa966239fa8918a838214ce78"},"schema_version":"1.0","source":{"id":"1511.06168","kind":"arxiv","version":5}},"canonical_sha256":"d8aef1c8ee75973622335c3bc4d30b1d1668d7d0ea04d5987774d904b1c3ae8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8aef1c8ee75973622335c3bc4d30b1d1668d7d0ea04d5987774d904b1c3ae8d","first_computed_at":"2026-05-18T00:54:20.693385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:20.693385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QNmds3ZyI+pikm7v5SmZPsU7DjiJXzE7Dln5MpYcafXKdLcxDhv6raWieQ/Qgmf2XNH7no1+OiMMcGIJv8ohCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:20.693747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06168","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f4e65af55da1121be7ba7459e32e097bef0990d00433dab6c0a02d9843e2301","sha256:526addc80e6fb0471d8127846b54765c626fd8775da1dee04e32d527a77ee136"],"state_sha256":"030d0f86304dee1a0f6b3b727892d88040a3cd0b84d439f9d60bd280824cd4e8"}